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MAXIMA is an intensive six-week REU program in interdisciplinary mathematics, funded by a three-year NSF REU grant and the IMA.

Students will work in teams of four on an open research problem in applied mathematics. Each team will be advised by a Macalester College Mathematics, Statistics, and Computer Science (MSCS) faculty member. Problems will be posed by University of Minnesota (UMN) researchers in fields outside of mathematics. Students will also be mentored by a postdoctoral fellow at the IMA.

The program is designed to allow students to experience the excitement of doing research that is relevant to another field. Students will learn how to formulate domain-specific questions in mathematical ways and assimilate the ability to communicate across disciplines. The program will develop mathematical skills and expository argumentation. By the end of the summer, each team will produce a written report, an oral presentation, and a research poster.

Eligibility

Students must be current sophomores and juniors who will be full-time undergraduate students as of September 2014, majoring in mathematics or a related field at a U.S. college or university.

Students must have taken multivariable calculus, linear algebra, and at least one upper-level undergraduate course (and preferably more). Exposure to computer science or statistics is also preferred. See the problem descriptions for further background requirements.

Students must be fully committed to the REU. Students may not engage in any other course work or employment for the duration of the program.

Nine spots are funded by the NSF; these are open to U.S. citizens and permanent residents. Three spots are funded by the IMA; these spots are open to U.S. citizens, permanent residents, and international students studying at U.S. institutions.

Women and underrepresented groups are particularly encouraged to apply.

RemunerationStudents receive a stipend of about ,000 and a travel allowance to/from the REU site. UMN campus housing and meals are provided at no additional cost. Support will also be provided to attend a national mathematics meeting to present the student research.

"What did you do today?" This simple question interests researchers in fields as diverse as psychology, sociology, urban planning, and health care. Traditionally, individuals participating in research studies recall and report this information via a (typically paper-based) trip/activity diary. These diaries are burdensome, prone to recall bias, and limit the quantity and quality of collected data. The widespread adoption of smartphone technology provides an exciting opportunity to improve the way we collect activity information. Specifically, a smartphone equipped with a GPS receiver and an accelerometer can record location and movements without any user input. In this project, students will participate in the development and implementation of mathematical, statistical and computational techniques to automatically detect, identify, and summarize attributes of daily activity and travel episodes using smartphone sensor data.

Through a research grant funded by the US Department of Transportation, Professor Wolfson's research team is currently developing the SmarTrAc app, which uses these data sources to compile and summarize an individual's daily trips and activities. SmarTrAc will free study participants from the drudgery of cataloging their activities via a diary. This enables researchers to ask more detailed information about choices and motivations. For example, if the application detects that a particular individual usually drives to work but sometimes takes the bus, then it would prompt the user to identify which factors determine their choice of mode of transportation.

Student participants will analyze GPS and accelerometer-derived time series data collected during pilot testing of SmarTrAC. They will tackle questions such as: 1) How does one automatically extract a set of distinct activities/trips from unlabeled time series data? 2) Is it possible to distinguish between multiple modes of transportation on the basis of GPS and/or accelerometer data? 3) Can smartphone sensor data be used to automatically infer the purpose of particular trips and activities?

Required background: Basic statistics, familiarity with statistical or numerical software such as R or MATLAB.

Useful Background: familiarity with Java (language of implementation of SmarTrAC), experience in one (or more) of regression modeling, machine learning, time series data, or mobile device programming.

People and technologies rely more and more on user­created datasets like Wikipedia. However, research has begun to reveal important cultural biases in these datasets. In this project, we will use state-­of-­the-­art techniques from the domains of artificial intelligence (AI) and natural language processing (NLP) to surface, quantify and visualize the similarities and differences in how various online encyclopedias describe the world.

We will analyze multiple language editions of Wikipedia (e.g. the English Wikipedia, the Hebrew Wikipedia, and the Arabic Wikipedia) as well as other online encyclopedias like Conservapedia, which describes itself as “written from a Christian fundamentalist viewpoint”, and Ecured, the Cuban government’s encyclopedia. We will investigate, for instance, the different descriptions of the topic "contraception" present in these encyclopedias, visualize these differences using information visualization approaches, and do this with "big data" methods that can handle the millions of articles in our dataset.

In this project, we will use numerical optimization and linear algebra techniques to devise representations of human poses via processing 3D information from multiple KINECT sensors. We will then map them to the body of a humanoid robot and program the robotic hardware to mimic the respective human poses.

Robots and robotic devices have become integral parts of our lives. They sweep floors, clean windows, perform surveillance, and assist in operating rooms. Future successful interactions will likely depend on enriching our communications repertoire to include important non-verbal modalities. Just as human interactions typically are not restricted only to simple commands or to simple statement/response dialogues, advances in sensor technologies and algorithmic procedures provide new ways to interact with robots. A natural human-robot coexistence must include the capacities to instruct robot companions and assistants by demonstration, to have them respond correctly to our gestures and expressions, and to have them recognize our intentions and our immediate situational needs.

Depth sensors such as the KINECT provide an excellent medium to realize robot learning by mapping human poses and gestures to equivalent robotic poses and gestures. Interpreting the KINECT sensor data is a nonlinear constrained optimization problem, known as inverse kinematics or motion retargeting. Current implementations use heuristic methods to interpret the data. We will apply a first-principles approach using established optimization and numerical linear algebra techniques to identify and map human poses.